Negation and contrapositive are two different things.

Conditional: P → C

Contrapositive: /C → /P

Inverse: /P → /C

Converse: C → P

Negation: P and /C

Unless is a negate sufficient indicator, you can pick either relata to negate and make the sufficient condition. They just choose the statement that is already negated because that is easier for most people to keep in their heads and easier to write out in lawgic.

Ex: Your car will be in the parking lot unless you did not lock it.

Relata 1: Your car will be in the parking lot [PARK]

Relata 2: You did NOT lock it [/LOCK]

Idicatoar: unless (group 3 negate sufficient).

Now, you have a choice here, you can pick either relata to negate and make the sufficient condition but which is easier to remember in your head?

LOCK → PARK (If you lock it your car will be in the parking lot)

/PARK → /LOCK (If you DO NOT lock it, your car will NOT be in the parking lot)

For me (and most people, I think), the first logical statement is much easier to keep track of in your head. Why go with the logical statement that you know will be a double negative? What if it ends up being a chained conditional? Not worth trying to keep organized in your head. Better to go with the easier statement and write out the contrapositive if and only if (lol, see what I did there?) you need it

No, that is not a negation, that is a contrapositive. Remember that a conditional statement and it's contrapositive are equivalents. For example for the statement "if you are a dog you have fur".

D = a dog

F = have fur

In lawgic "if you are a dog you have fur" becomes "D→F" and the contrapositive of "if you don't have fur you are not a dog" becomes "/F→/D". You see how they're really just saying the same thing? You can tell they are contrapositives because they can both be true at the same time. Obviously if you need fur to be a dog then if you don't have fur, you can't be a dog.

On the other hand, the negation of "if you have a dog you have fur" would be "it is not the case that if you have a dog you have fur" which translates to lawgic as "D and /F" that is to day "there is a dog that has no fur". You can tell its a negation because "D→F" and "D and /F" cannot both be true at the same time. You cannot say "if you are a dog you have fur" and then also say "here is a dog with not fur", one of them must be false.

Hope that helps!

nvm

Hey, I actually figured it out in my own. Arguments are meant to be persuasive, they should be trying to get you to think/feel/believe/do something (the conclusion). That’s why “ they should stop producing food waste and shut down operations immediately” is the conclusion and “ But this is not a sustainable, long term solution.” is not. The former is prescriptive while the latter isn’t. In fact when you treat latter as a premise it makes even more sense. “But this is not a sustainable, long term solution [therefore] they should stop producing food waste and shut down operations immediately”. See how that works as a premise to conclusion relationship? Try the reverse and you’ll see it won’t work at all. It’s a good test to make sure you’re relating the claims correctly.

For 3.1 I wrote:

Context: The restaurants on the main block are all temporarily storing its food waste in its backyard.

Premise [P1]: Since none of them have devised a suitable recycling or disposal plan

Sub Conclusion/Major Premise [SC1]: they should stop producing food waste and shut down operations immediately.

Conclusion [C1]: But this is not a sustainable, long term solution.

My thinking was P1 therefore SC1, therefore C1. Can someone explain why P1 does not support SC1 and why "they should stop producing food waste and shut down operations immediately." is the main conclusion rather than a sub conclusion?

Think of "major" and "minor" as relata. A sub-sub conclusion can be a major premise to the sub-conclusion but a minor premise to the main conclusion. Kind of like how in an earlier example he showed that a woman can be daughter to a mother or a mother to a daughter, the role is relational. Does that make sense?

"Fluffer is adorable" isn't the conclusion because when related to "Fluffers is cute" it is a premise claim/relata. "Fluffer is cute" is the only conclusion claim/relata that is not also a premise.